The study of computer algorithms which admit geometric descriptions, and geometric problems arising in association with such algorithms. The two major classes of problems are (a) efficient design of algorithms and data classes using geometric concepts and (b) representation and modelling of curves ...

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7
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2answers
153 views

How to check if polylines can be untangled?

In a program I'm writing I need to be able to check whether a straight line between two points is homotopic to a polyline between them. For example in the below example the first one is equivalent to ...
0
votes
2answers
181 views

Proof of the following: How many $(n-2)$ dimensional faces from a corner of a hypercube

I asked a question earlier regarding the number of $(n-2)$ dimensional faces exiting a corner of an $n$ dimensional hypercube. (For example the number of points in a corner of a square, or the number ...
1
vote
0answers
86 views

Optimal bounding boxes selection for $N$ rectangles

Suppose that I have $n$ straight rectangles on a plane $r_i = (x_i,y_i,w_i,h_i)$. Each rectangle has a cost function, its area $A(r_i) = w_i \cdot h_i $. I can also "merge" 2 or more rectangles into ...
0
votes
0answers
34 views

Polytime programming

Given a linear system of the form: $$x_r = a$$ $$x_j = b$$ $$c_1x_1 + c_2x_2 ... c_nx_n = n$$ $$x_1 + x_2 + x_3 ... x_n = k $$ $$0 \leq a,b,x_1, x_2, x_3 ... x_n \leq 1$$ $$k \geq 0$$ How quickly ...
3
votes
1answer
82 views

Computing with graphs in surfaces

I am currently working on a research project involving a polynomial defined for graphs in surfaces, similar to the Tutte polynomial, except with terms accounting for the embedding. At the moment, it ...
4
votes
1answer
88 views

Covering all the edges of a hypercube?

Consider an arbitrary $n$- dimensional hypercube: If we select $n - 1$ corners of that hypercube and highlight all $(n - 2)$ dimensional elements that originate from each of the corners is it ...
2
votes
1answer
69 views

A method to test for uniform distribution over a convex polytope

Assuming I have a convex polytope defined as the intersection of $Ax=b$ and $x>0$ and I have a way to sample points from this object, is there a way I can test for uniformity of these sampled ...
0
votes
1answer
982 views

How to find rotation angles along X,Y,Z axes with a known vector to bring the axes to correct situation

I am working with 3d point data. When I checked the data I realized that there is some error on my data and need to do some kind of rotational rectification because the points which should be ...
0
votes
0answers
144 views

how to get optimal vector, which is parallel to intersection line of many plane (Least Square way)

My idea is to construct the best optimal 3D line representing the intersection of many 3D planes. (As we know, due to fitting errors or data errors, the fitted planes might not intersect exactly ...
0
votes
1answer
223 views

my plane is not vertical, How to update 3D coordinate of point cloud to lie on a 3D vertical plane

I have a bunch of points lying on a vertical plane. In reality this plane should be exactly vertical. But, when I visualize the point cloud, there is a slight inclination (nearly 2 degrees) ...
4
votes
1answer
48 views

How can I geometrically (or geographically) group items together?

I'm a programmer, and I'm working on a project that takes a bunch of photos and separates them into groups by their gps coordinates. I have no experience in things like geometric group theory so I'm ...
1
vote
1answer
100 views

What is the typical method for sampling uniformly in a convex polytope

The polytope in my case is the intersection of the k-plane $Ax=b$ and $\{x>0\}$ where $A$ is the constraint matrix and $b$ is some solution. I'd like to find a method that is fast and efficient for ...
1
vote
0answers
59 views

Checking if a binary vector lies in the affine span of given binary vectors

Let $x_1, \ldots,x_N \in \{0,1\}^D$ be $N$ binary vectors, assumed affinely independent (in the field of reals). Is there an efficient algorithm for determining whether a new binary vector $x_{N+1}$ ...
2
votes
0answers
91 views

RANSAC line fitting (3d) by line segments (3d)

I am having many 3d line segments. some of them are nearly parallel and some are oriented in to different direction. I want to avoid outliers and to get the best line 3d to represent the given ...
3
votes
3answers
818 views

Finding the major and minor axis vertices for an ellipse given two conjugate diameters?

I've been googling, searching forums and looking in my old algebra/trig books to try to understand how to find the end points to the major and minor axis of an ellipse given the end points of two ...
0
votes
1answer
69 views

Generating Vectors under Constraints on 1 and 2 norm

Update: I left out some important information in my previous description... I am actually dealing with a special problem, which is better described as follows: Given user-specified parameters ...
2
votes
1answer
258 views

Distance between point and plane & orthogonal projection matrix

I am poor in mathematics and want to learn few fundamental ethics to understand some of advanced things; For plane $i$, denote $n_i\in\mathbb{R}^3$ and $o_i\in\mathbb{R}^3$ respectively as its normal ...
4
votes
1answer
132 views

Potential Division by zero in the construction of NURBS basis functions: how to handle?

Some background context In reading about NURBS I saw the definition that the B-Spline basis functions are defined by a recurrence relation. $N_{i,n} (u)= f_{i,n}(u) N_{i,n-1}(u) + g_{i+1,n}(u) ...
2
votes
1answer
421 views

Angle between different rays (3d line segments) and computing their angular relationships

I have several positions (say A,B,C,..) and I know their coordinates (3d). From each point, if a certain ray is passing in a way to converge them at a given (known) point (say O). This point O ...
1
vote
0answers
82 views

viewing ray geometry - with multiple aerial photographs

I am working with multiple aerial images. My idea is to model 3d objects (only upper parts). I am having known orientation parameters. As I am new to this field so that, I want to clarify few general ...
4
votes
1answer
142 views

Intersection of planes by forming 3d lines

If I have $n$ known planes (known normal vector and a point on a plane) that intersect each other in such a way so as to form closely located 3D lines, then (1). To get a common single 3D line to ...
3
votes
1answer
146 views

Partitioning a set of rectangles into disjoint subsets each of which consists of disjoint rectangles

Suppose we have a list $R$ of axis-aligned rectangles in the plane. There is the well-known problem of determining the maximum subset of $R$ which consists of disjoint rectangles; this problem is ...
2
votes
1answer
112 views

incident angles between rays, falling on an oblique plane

I am having really two simple questions, but following two things are confusing me. Question 1 If I know plane parameter (v3) of a given plane (say AB); if a pair of rays are incident at a ...
4
votes
0answers
118 views

Biggest ball included in an intersection of balls

I would like to prove that for any family of balls $\{B(c_i,r_i)\}_i \subset \mathbb{R}^d$ such that $\{c_1, \dots, c_n\} \subset \bigcap_i B(c_i,r_i) $ and $\forall i, r_i \geq 1$, there exists a ...
1
vote
1answer
50 views

What do we call the angular arcs between two edges of triangles?

I've been trying to find a geometry library for java which is as high level as describing angles between adjacent sides of triangles given 3 sides. So, what do we call such kind of arcs. In many ...
2
votes
2answers
104 views

Books for Geometry processing

Please suggest some basic books on geometry processing. I want to learn this subject for learning algorithms in 3d mesh generation and graphics. Please suggest me subjects or areas of mathematics i ...
2
votes
1answer
80 views

Computational geometry

Computational geometry? (Computational geometry) Given a set of n randomly scattered points for even n = 2,4,6,...,50 . Find the maximum number of lines between the pairs of nodes in such a way the ...
2
votes
1answer
388 views

Circle Packing: Unsolved Problem in Geometry?

Graham and Sloane minimize the second moment of the centres of a number discs in order to maximize their compactness. They use computational geometry techniques to find the optimal packings for ...
1
vote
2answers
429 views

Finding the tangents common to two rotated ellipses?

Is there a way to find the four tangents that two rotated ellipses share? I believe that if two ellipses do not intersect and do not contain one another, they will have four tangents in common and I ...
0
votes
1answer
315 views

closest pair in N-Dimensional

I have to find the closest pair in n-dimension, and I have problem in the combine steps. I use the divide and conquer.I first choose the median x, and split it into left and right part, and then find ...
1
vote
2answers
94 views

Approximating Euclidean geometry, restricted to $\mathbb{Q}$

I'm having trouble putting this into a fully coherent question, so I'll give the broad question, then a few bullet points to give you a better idea of what I'm asking. I'm looking for a line of ...
3
votes
1answer
74 views

Linear, Bi-linear or better

I have been writing some code to do some interpolation of 2D data on an irregular grid. So far what I have done is: Triangulate the known points using Delaunay. Find the vertices of the triangles ...
1
vote
1answer
106 views

Winding a space curve

Can I find parametric equations for a curve that is winding another curve, which I know -- let's say it's $\vec{f}(t) = (x(t), y(t), z(t)) = \{\sin (t)+2 \sin (2 t), \cos (t)-2 \cos (2 t), -\sin (3 ...
2
votes
1answer
37 views

Fragemented linear feature alignment technique

I am having set of linear features lie on a plane (it does not a matter whether the pane is vertical or horizontal). all linear features are either parallel or othogonal to the vertical axis or ...
0
votes
1answer
154 views

Perpendicular to a vector at point on the vector

I am working with a model where I have to calculate a perpendicular to a vector through two points $\mathrm{P_1}$ and $\mathrm{P_2}$ (3d) at point $\mathrm{P_3}$ on the line joining these points. ...
1
vote
2answers
105 views

How to find co ordinates of a triangle after increasing the area by a factor of $\alpha$?

i am given with a triangle $\{(x_1,y_1),(x_2,y_2),(x_3,y_3)\}$ and the area need to be increased by a factor $\alpha$. can i anyone let me know formula to find the co ordinates of new triangle? There ...
2
votes
1answer
179 views

Lloyd's algorithm in normed vector spaces

How do I run Lloyd's algorithm in a normed vector space? The space: L*a*b* color space, finite sRGB segment, $R^3$ The distance metric: CIE94 using L*C*h* information derived from the L*a*b* ...
2
votes
1answer
44 views

How to estimate orientation errors of an image with respect to known data (line features)

I think this is very simple but for me, it is confusing to figure out a way. Here is my problem. I have been given a 3d line segment list obtained from a field survey. So I know each end point ...
1
vote
1answer
99 views

angle between steepest gradient of two plane

IF I have two 3d planes such as Oab and Oa'b'. If these two planes intersect a horizontal plane and the intersection of each plane makes AB and A'B' lines. then, Does the angle between AB, A'B' ...
0
votes
1answer
65 views

$2$ planes and angle between them

IF I have two $3d$ planes such as Oab and Oa'b'. If these two planes intersect a horizontal plane and the intersection of each plane makes AB and A'B' lines. then, Does the angle between AB, ...
0
votes
1answer
74 views

obtainig a line 3D from multi view geometry

If I have been given multiple view images having known orientation parameters, then from a selected image line segment (corresponding line segments from each image) how could I compute a line 3D in ...
0
votes
1answer
108 views

Steepest slope gradient of a vertical plane

I know the steepest slope gradient (Azimuth) of a 3D plane can be obtained by projecting normal vector onto XY Plane. So, when the plane is slant, the steepest gradient will be a some value. ...
1
vote
1answer
85 views

Predicting the size of epsilon-net in SU(2)

I'm writing an algorithm that takes as input a finite set of matrices in SU(2) and consequently tries to generate an '$\epsilon$-net' by computing all possible matrix products (up to a given depth). ...
2
votes
0answers
76 views

Calculation of the fundamental group from triangulations

Is there - say, for a triangulable surface - a concrete algorithm how to calculate the fundamental group of the surface from a given triangulation, seen as a graph (of its 1-skeleton), given as an ...
5
votes
2answers
90 views

Find the most vertical line in a point set in $O(n \log n)$ time

Input: a set of $n$ points in general position in $\mathbb{R}^2$. Output: the pair of points whose slope has the largest magnitude. Time constraint: $O(n \log n)$ or better. Please don't spoil the ...
2
votes
1answer
261 views

Obtaining Least square adjusted single line by intersecting many 3D planes

I am working with many 3D planes and looking for a Least square solution for below case. IF I am having many number of 3D planes knowing only one point and the normal vector (for eg. O1 and N1), ...
0
votes
0answers
62 views

transformation function using genetic programming

If I have a set of points in two spaces, say set $A$ contains 50 points and set $B$ contains 50 points. I have to find a transformation function such that if I transform the points in set $A$ using ...
1
vote
0answers
54 views

How to estimate error pattern of a set of line segments with respect to given reference segments (2D case)

I am having set of pair of line segments (2D). Though each pair should be coincided on top of each other they are not so. I have been the reference data and then I extracted other line segments ...
1
vote
2answers
382 views

Determing the distance from a line segment to a point in 3-space

Imagine I have a line segment defined by endpoints $p_1$ and $p_2$, and some 3-space coordinate $q$. Is there a robust (in the sense of never giving divide-by-zero errors) way to quickly determine ...
3
votes
0answers
47 views

For which coverings by “geometrically nice” sets does the nerve admit “Vietoris-Rips-like” approximations?

It is well known that the nerve (or Čech complex) of a covering by metric balls is nicely approximated by the Vietoris-Rips complex. Being a flag complex on its 1-simplices, the latter is ...